M4890139 Mersenne number exponent details

Residue

Status

L-L

531026AB11510B9E

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷¹	97.7637	67.6056%	410000	11070000	0.1991	3.5383%	97.9629	68.7518%	1.1462%
PrimeNet	2⁶¹	0.0628	62.2951%	22000	450000	0.0091	3.3010%	0.0719	63.5397%	1.2446%
GPU72	2⁶⁵	1.4919	64.6154%	32000	700000	0.0137	2.3732%	1.5057	65.4551%	0.8397%
Difference	+6	+96.2718	+2.9902%	+378000	+10370000	+0.1854	+1.1651%	+96.4572	+3.2967%	+3.2967%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

97.7637

67.6056%

410000

11070000

0.1991

3.5383%

97.9629

68.7518%

1.1462%

PrimeNet

2⁶¹

0.0628

62.2951%

22000

450000

0.0091

3.3010%

0.0719

63.5397%

1.2446%

GPU72

2⁶⁵

1.4919

64.6154%

32000

700000

0.0137

2.3732%

1.5057

65.4551%

0.8397%

Difference

+96.2718

+2.9902%

+378000

+10370000

+0.1854

+1.1651%

+96.4572

+3.2967%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-25T14:45:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	0.888%
2014-01-12T13:00:00	David Campeau	i5-2500k	410000	11070000		-		-	-	0.199	-	-	3.538%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.063	-	-
2010-04-16T20:18:00	garo	north	2⁶¹	2⁶²		-	-	0.063	-	-
2011-10-09T23:38:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.326	-	-
2016-02-23T16:39:03	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.201	-	-
2015-01-07T16:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.401	-	-
2015-01-07T16:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.764	-	-
2015-07-22T21:15:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.528	-	-
2017-10-31T15:30:51	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	3.056	-	-
2018-05-08T11:46:41	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	6.112	-	-
2018-06-09T17:36:52	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	12.22	-	-
2018-06-09T17:36:52	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	24.45	-	-
2020-12-03T20:03:57	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	48.90	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.886 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.886 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.346	70.740%
25	50000	0.032	96.848%
30	250000	0.002	99.798%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.886

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-04-14T10:27:00	sasaki3	ssk_saver	50000	5000000						3	0.629
2014-03-06T18:48:00	S36049	Wolle5	50000	5000000						3	0.629
2017-04-27T10:57:45	Claude Portenier	Petit-Idiot	50000	5000000						3	0.629

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-08T00:00:00	ANONYMOUS	v4_computers	531026AB11510B9E	0.678
2000-04-12T00:00:00	ANONYMOUS	v4_computers	531026AB11510B9E	0.678

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 410000, B2 = 11070000 (P-1 stage 2)

B1 = 410000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront